Twisted-mass lattice QCD with mass non-degenerate quarks

TL;DR

This paper extends the benefits of maximally twisted lattice QCD, including automatic O(a) improvement and symmetry properties, to the case of non-degenerate quark masses, enhancing its applicability.

Contribution

It demonstrates that the advantageous properties of maximally twisted lattice QCD hold even with mass non-degenerate quark pairs, broadening its practical use.

Findings

Positive fermion determinant for non-degenerate quarks

O(a) improvement persists with mass non-degeneracy

Symmetry properties extend to non-degenerate case

Abstract

The maximally twisted lattice QCD action of an $SU_f(2)$ doublet of mass degenerate Wilson quarks gives rise to a real positive fermion determinant and it is invariant under the product of standard parity times the change of sign of the coefficient of the Wilson term. The existence of this spurionic symmetry implies that O($a$) improvement is either automatic or achieved through simple linear combinations of quantities taken with opposite external three-momenta. We show that in the case of maximal twist all these nice results can be extended to the more interesting case of a mass non-degenerate quark pair.